Fate/EXTRA/Headscratchers

Why is it that even though you know the identity of Leo's Servant practically from the start of the War you don't get a major boost to the Matrix?
- Because you only know his name. The protagonist was way too busy with everything to have time to research someone they didn't expect to fight. Also, a name won't tell you how someone fights or what their skills are.
  - Won't it still tell you a vast amount about them such as temperament, style and relations with other Servants? Unlike Shinji, Leo doesn't see any need to hide books so it should be easy to go to the library and look up this person.
  - Well, the protagonist does look up on him a bit if you go to the library after Leo tells you, but that's just his character biography. Also, the protagonist is busy with Shinji at the time, and since Leo isn't their opponent, why bother looking further when they might never fight him at all? At that point, they're still pretty weak, so all their attention is probably focused just on surviving that first week.
  - It's not as if they don't have time later, though; regardless of how you do have to prep for your current opponent, it's unlikely you don't have time to hunt for info in the library during the subsequent weeks. That said, the later opponents generally require you to fight them in the Arena (and survive, obviously) in order to gather data, so having to do the same with Gawain as opposed to just reading up on him isn't unusual.
Regular Masters have the 'generic Master' template, and the MC's slight difference is a sign of their being More Than Meets the Eye. They also say that only powerful hackers are capable of altering their avatars, which makes sense for Rin, Leo, presumably Rani and Julius, ect. Does this mean the Monster Clown and the non-denominational Church Militant are capable of taking time out from their psychoses to so heavily customize their appearance within the Moon Cell?
- Magical hacking still depends on the number of Magical Circuits you have. Which is why it's magical hacking... and not, you know, regular hacking. The mana depletion caused regular magecraft to die out, but it was replaced by spiritual hacking and other methods of using magical circuits. The avatars are probably determined by your skill in customization and your level of circuits.
  - Not really, if the characters are to be believed. Your avatar might be altered to a certain extent like the Protagonists', but it's clearly a conscious choice for the others: Shinji's abilities as a hacker (one assumes they mean spirit hacker, since it's implied that everyone except you came as magi) are noted when they talk about customizing his avatar, Julius is mentioned as having hacked Kuzuki's profile, presumably including the associated avatar's appearance (unless you think said teacher always wore that coat), and Rin's blonde hair in real life is unlikely to have changed to black in the Moon Cell unless she did it intentionally. Rin (and Rani, in her path) says that a magi's avatar is determined by aptitude, but that doesn't mean their avatar automatically molds to their chosen form. Advanced magi like Rin and Leo can make avatars that are perfect copies of their real selves, while most others are stuck with normal avatars because they lack the skill to manipulate the virtual world; the exceptions are like Alice, who lacked the limitations of a physical body and could customize her 'avatar' without the constraints of a real-world counterpart. Even if Ronnie and Gatou were powerful magi they'd still have to intentionally shape their avatars, which seems a little unlikely given their apparent inability to focus on anything but their respective obsessions.
While stalking Julius and Assassin to discover the source of Assassin's invisibility, you and you Servant "hide in the shadows" to remain unseen. There are no shadows in the field, you're restricted to the actual map which means you can't hide outside of the walls and occasional plateaus (which lack large rocks or other features), and the walls themselves are transparent. How are these trained killers failing to see you? Or perhaps more to the point, since it's implied Assassin knows you're there, how does the Protagonist (and their Servant) think that these transparent walls are going to conceal them?
- The lack of shadows is likely a limitation of the PSP's hardware, and even if the walls are transparent (it's also possible that they're only transparent to the players, not the characters), you're usually still out of their line of sight. Also, Julius always struck me as being rather careless, afflicted with a bad case of tunnel vision or simply not being very good at sensing things (he doesn't notice Rin, who should have been in his line of sight, until she introduces herself during the fake Bad End after the second week).
  - It's implied that Assassin knows that you are there; he's amused and wants to see what you can do.
  - Yes, the OP made it clear that Assassin knew about the stalking; the core of the question is still "Seriously, the Black Scorpion is unaware of you guys?" and "Also the walls are transparent." It seems unlikely the walls are only transparent to the player since your Servant will remark on the levels in ways that imply the corridors are translucent: In example, Archer's comment about the next stage being an ice castle is made on a level where the castle would only be visible if the walls are actually see-through. It just seems odd that your random protag and their non-Assassin Servant could avoid the detection of a trained assassin, though Julius does seem aggravated after dealing with Rin/Rani and might not be as alert as he'd normally be.
  - It's also implied that Julius isn't a mage, or at least he's not a good one: When he kills people it's physical, and when you show Leo the lapel pin he says that the pin connected Julius to the Harway databanks and avoided the need for Julius to be a skilled mage. If magic talent influences your ability in the Moon Cell, Julius' lack thereof could explain why he didn't see Rin (a talented magi) coming, why he couldn't kill Rin/Rani (a magical construct) in the fifth week, and why he seems to have a hard time detecting your Servant (while spying on him and Assassin, Julius being surprised to survived Assassin in the sealed space as if he didn't know your Servant intervened). So Assassin knows you're there but he's having too much fun to spoil the game, and Julius is losing his cool enough to let it impact his already less-than-stellar mystic abilities.
How do some of the other Masters, specifically the boy on the second floor by the classrooms (who talks about being there to gather data) and the girl by classroom 1-A seem to know about you being a digital ghost, or at least something like it? They call you "just a memory" and "the ghost in the machine" as soon as the War begins, long before you realize there's anything weird about yourself besides the amnesia thing.
- It's possible that they're hackers specialized in information gathering (their non-unique appearance probably means they're not powerful ones, though). The MCs semi-unique appearance as well as some of the other discrepancies would have struck them as odd, which meant they studied the MCs more closely, which lead to them guessing the MCs are virtual ghosts. The others didn't notice because they're focused on the War and their respective opponents.